It is a well-known conjecture that the number of of twin primes below $n$ is asymptotically equal to
\[C_2 \frac{n}{(\log n)^2}\] with $C_2 = 0.66...$ (the value of a certain infinite product).
See eg this wikipedia page http://en.wikipedia.org/wiki/Twin_prime that also mentions Brun's upper bound which is perhaps what you refer to.
p.s. I am not sure if this answers your question; if not please clarify/narrow down your question.